Maths topic

place value

Place value tells us what a digit is worth because of where it sits in a number.

Practise place value Explore place value houses Back to topics

the big idea

Digits build numbers. A digit has a place, and that place tells us its value. In 358, the 3 is in the hundreds place, so it is worth 300.

digit one symbol like 3
place hundreds place
value 3 hundreds = 300

build a number

Choose a number and watch each digit move into its place value house.

thousands 0 0
hundreds 3 300
tens 5 50
ones 8 8
1000s
0
100s
10s
1s

358

expanded form300 + 50 + 8 digit value3 in the hundreds place means 300. zeroNo zero placeholders in 358.
number

place value houses

A place value house keeps each digit in the correct place.

  • Start at the right with ones.
  • Move left to tens, hundreds and thousands.
  • Each move left is ten times larger than the place before it.
thousands 0 0
hundreds 3 300
tens 5 50
ones 8 8

358 has 3 hundreds, 5 tens and 8 ones.

same digit, different value

The digit does not change, but its value changes when it moves to a different place.

  • 5 in the ones place means 5.
  • 5 in the tens place means 50.
  • 5 in the hundreds place means 500.
  • 5 in the thousands place means 5000.
5 ones 5
50 tens 5 tens
500 hundreds 5 hundreds
5,000 thousands 5 thousands

expanded form

Expanded form splits a number into the value of each digit.

  • 4,382 has 4 thousands, 3 hundreds, 8 tens and 2 ones.
  • 4,382 = 4000 + 300 + 80 + 2.
  • Expanded form helps us see what each digit is worth.
thousands 4 4,000
hundreds 3 300
tens 8 80
ones 2 2
4,382 = 4000 + 300 + 80 + 2

zero as a placeholder

Zero can hold an empty place so the other digits stay in the correct places.

  • In 304, the 0 shows there are no tens.
  • The 0 keeps the 3 in the hundreds place.
  • 304 is different from 34 because the digits are in different places.
304
thousands 0 0
hundreds 3 300
tens 0 0
ones 4 4
0 tens keeps the 3 in hundreds
34
thousands 0 0
hundreds 0 0
tens 3 30
ones 4 4
3 tens and 4 ones

regrouping with base ten

Our number system groups in tens. Ten of one place can be exchanged for one of the next place.

  • 10 ones can be regrouped as 1 ten.
  • 10 tens can be regrouped as 1 hundred.
  • MAB blocks help us see these exchanges.
10 ones
= 1 ten
10 tens
= 1 hundred

comparing numbers

To compare numbers, start with the largest place and move right until the digits are different.

  • Compare thousands first, then hundreds, then tens, then ones.
  • In 5,204 and 5,240, the thousands and hundreds match.
  • The tens place is different, so 5,240 is larger.
5,204
thousands 5 5,000
hundreds 2 200
tens 0 0
ones 4 4
<
5,240
thousands 5 5,000
hundreds 2 200
tens 4 40
ones 0 0

The tens place is the first different place.

place value words

These words help us read, build and compare numbers.

1 digit symbol

one symbol used to write numbers

2 ones 1s

the place for single ones

3 tens 10s

the place for groups of ten

4 hundreds 100s

the place for groups of one hundred

5 thousands 1000s

the place for groups of one thousand

6 expanded form split value

a number split into the value of each digit

7 placeholder 0 holds place

a zero that keeps other digits in the correct places

place value facts

10 ones 1 ten
10 tens 1 hundred
10 hundreds 1 thousand
358 300 + 50 + 8
fact In 507, the 0 holds the tens place
fact Compare from the largest place first

real world examples

money reading dollars, tens of dollars and hundreds of dollars
addresses understanding numbers on houses and streets
sport comparing scores with hundreds and thousands
population reading large town or city numbers
measurement reading metres, centimetres or millimetres
shopping comparing prices by the largest place first

quick place value quiz

Try a few place value ideas. This quiz only asks about ideas shown on this page.

In 358, what is the value of the digit 3?

Which expanded form matches 4,382?

What does the 0 do in 304?

What can 10 ones be regrouped as?

When comparing numbers, where should you start?